Ultra-micrometer.

R. Whiddington. The Ultra-Micrometer; an application of the Thermionic Valve to the measurements of very small distances. Phil. Mag. 30, p. 634. (1920).

If one takes two coupled generator circuits oscillating with thermionic valves, giving a high frequency (about \(10^6\) periods per second), and tunes them slightly apart from one another, beats are obtained, the number of which is equal to the difference between the numbers of oscillations of the two generators. If this difference lies within the range of audio frequency, then in a telephone connected into the anode circuit of one of the generators one can hear a sound whose number of vibrations is equal to the aforementioned difference in the numbers of oscillations. It is clear that very small changes in the capacitance of the oscillatory circuit produce a quite appreciable change in the pitch of the sound. Changes in pitch were measured by the method of beats with sounds of definite pitch, and a difference in pitch of 1 vibration per second can be detected. The sensitivity of this method is:

\[ \frac{dN}{dx}=\frac{1}{2(xLS)^{1/2}}=\frac{N}{2x} \]

where \(L\) is the self-inductance of the circuit, \(S\) is the area of a variable (plane) condenser, and \(x\) is the distance between its plates.

Putting \(N=10^6\), \(dN=1\), \(x=2.5\cdot 10^{-3}\) cm, we obtain \(dx=5\cdot 10^{-9}\) cm. In fact, the author succeeded in observing a change in distance of the order of \(10^{-8}\) cm, caused by a load of 1 mgr placed on a lever 12.5 cm long, bending the support of one of the condenser plates.

S. Rzhevkin.